2 Trigonometric Ratios and Special Angles PDF

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Trigonometric Ratios and Special Angles

Learning Goal: By the end of this lesson, students will have reexamined the special angles in radians, and reviewed calculating their sin, cos, tan, csc, sec or cot ratio. 1. Evaluate each of the following correct to 4 decimal places. 𝜋 a. sin 32° b. tan 2.1 c. sec

d. cot 121°

5

e. csc 3.2

f.

cos

3𝜋 7

g. csc

4𝜋

h. sec 153°

9

Special Angles - degrees sin 45° = cos 45° = tan 45° = sin 60° =

sin 30° =

cos 60° =

cos 30° =

tan 60° =

tan 30° =

2. Calculate each of the following, exactly. a. tan 225° b. csc 330°

Work: pg. 216 (3bd, 4bd, 5cd, 6ad, 8, 9, 11a, 12a)

c. cos 240°

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MHF4U

Trigonometric Ratios and Special Angles

Special Angles - radians sin

𝜋 = 4

𝜋 cos = 4 𝜋 tan = 4

3. Evaluate exactly. 5𝜋 a. cos

5𝜋 6

cot

𝜋 = 3

sin

𝜋 = 6

cos

𝜋 = 3

cos

𝜋 = 6

tan

𝜋 = 3

tan

𝜋 = 6

b. csc

4

d. sin

sin

7𝜋 4

− cos2

7𝜋 6

Work: pg. 216 (3bd, 4bd, 5cd, 6ad, 8, 9, 11a, 12a)

5𝜋

3

c. tan

5𝜋 6

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Trigonometric Ratios and Special Angles 𝜋

To find the trigonometric ratios of 0° (0 rad) or 90° ( 𝑟𝑎𝑑) use the unit circle and the 2 indicated properties (pictured right).

sin 0° =

csc 0° =

sin 90° =

csc 90° =

cos 0° =

sec 0° =

cos 90° =

sec 90° =

tan 0° =

cot 0° =

tan 90° =

cot 90° =

4. Evaluate each of the following exactly. a. cos 180° b. sin 270° c. tan 𝜋

Work: pg. 216 (3bd, 4bd, 5cd, 6ad, 8, 9, 11a, 12a)

d. csc

3𝜋 2

e. tan 2𝜋...